The present invention relates to communications methods and apparatus, and more particularly, to methods and apparatus for receiving communications signals subject to noise such as those typically found in wireless communication systems. Wireless communications systems are commonly employed to provide voice and data communications to subscribers. For example, analog cellular radiotelephone systems, such as those designated AMPS, ETACS, NMT-450, and NMT-900, have long been deployed successfully throughout the world. Digital cellular radiotelephone systems such as those conforming to the North American standard IS-54 and the European standard GSM have been in service since the early 1990""s. More recently, a wide variety of wireless digital services broadly labeled as PCS (Personal Communications Services) have been introduced, including advanced digital cellular systems conforming to standards such as IS-136 and IS-95, lower-power systems such as DECT (Digital Enhanced Cordless Telephone) and data communications services such as CDPD (Cellular Digital Packet Data). These and other systems are described in The Mobile Communications Handbook, edited by Gibson and published by CRC Press (1996).
Wireless communications systems such as cellular radiotelephone systems typically include a plurality of communication channels which may be established between a first transceiver (such as a base station) and a second transceiver (such as a mobile terminal). The communication channels typically are subject to performance-degrading environmental effects such as multi-path fading and additive disturbances. These various sources of additive disturbances may come from a variety of sources including thermal noise, a co-channel interferer and an adjacent-channel interferer.
The dynamic characteristics of the radio channel present difficulties in estimating the channel to allow for decoding of information contained in the received signal. Often, in wireless mobile radio systems, known data sequences are inserted periodically into the transmitted information sequences. Such data sequences are commonly called synchronizing sequences or training sequences and are typically provided at the beginning and/or in the middle of a frame of data or a burst of data. Channel estimation may be carried out using the synchronizing sequences and other known parameters to estimate the impact the channel has on the transmitted signal. Least square estimation may be an efficient way of estimating the channel impulse response in the presence of additive white Gaussian noise. However, as the noise becomes non-white, or colored, these techniques may become less effective.
To extract the transmitted signal (or symbols) from the received signal, the receiver of a mobile terminal typically includes a demodulator which may be a coherent demodulator such as a maximum likelihood sequence estimation (MLSE) demodulator (or equalizer). To adapt to the channel variation from each data burst to the next, an associated channel estimator is typically provided for the demodulator. The channel estimator typically operates using known transmitted symbols.
At any given time, the kind of disturbances (co-channel interferences, adjacent-channel interference, or thermal noise) that dominates in the received signal is generally unknown. The typical approach is to design the demodulator or the equalizer in the receiver assuming the dominant disturbance is white (i.e. uncorrelated in time), hoping that it will suffice well even when the disturbance is somewhat colored.
For example, consider the receiver model depicted in FIG. 1. A signal y(t) is first filtered in an analog receive filter 105 having a transfer function p(t) to provide a received signal r(t) which is downsampled to a symbol rate received signal r(n) before processing in the equalizer 110 to get a signal estimate sest(u). As used herein, the term xe2x80x9csymbol ratexe2x80x9d encompasses both the symbol transmission rate and multiples thereof. The symbol-rate downsampled discrete-time received signal r(n) is given by:                               r          ⁢                      xe2x80x83                    ⁢                      (            n            )                          =                                            ∑                              k                =                0                                            L                -                1                                      ⁢                          xe2x80x83                        ⁢                          c              ⁢                              xe2x80x83                            ⁢                              (                k                )                            ⁢                              xe2x80x83                            ⁢              s              ⁢                              xe2x80x83                            ⁢                              (                                  n                  -                  k                                )                                              +                      v            ⁢                          xe2x80x83                        ⁢                          (              n              )                                                          (        1        )            
where c(k) are the L coefficients of the baseband channel, s(n) are the transmitted symbols, and v(n) is a disturbance signal.
As noted above, to aid in estimating the channel c(k) at the receiver, the transmitter typically transmits a synchronization signal including a number of known symbols: {s(n)}n=n0n0+Mxe2x88x921. The channel coefficients, c(k)""s, are then estimated using the known transmitted symbols {s(n)}n=n0n0+Mxe2x88x921 and the known received signal {r(n)}n=n0n0+Mxe2x88x921. Generally, this is done by assuming that the disturbance v(n) is white, in other words, that the auto-correlation of v(n), xcfx81vv(k)=xcex4(k). Based on this assumption, the maximum likelihood (ML) estimate, expected to be the optimal estimate, of the c(k)""s is the least-squares estimate.
The auto-correlation function of the disturbance v(n) may be defined as:
xcfx81vv(k)=E{v(n)v*(nxe2x88x92k)}xe2x80x83xe2x80x83(2)
where k is the auto-correlation lag and E{ } represents the expected value. It is known that the least-squares estimate may be obtained as the solution to the following optimization criteria:                                                         c              ^                        LS                    ⁢                      xe2x80x83                    ⁢                      (            k            )                          =                                                         c              ⁢                              xe2x80x83                            ⁢                              (                k                )                                                    arg              ⁢                              xe2x80x83                            ⁢              min                                ⁢                      xe2x80x83                    ⁢                                    ∑                              n                =                                  n0                  +                  L                                                            n0                +                M                -                1                                      ⁢                          xe2x80x83                        ⁢                                          "LeftBracketingBar"                                                      r                    ⁢                                          xe2x80x83                                        ⁢                                          (                      n                      )                                                        -                                                            r                      ^                                        ⁡                                          [                                                                        n                          |                                                      n                            -                            1                                                                          ;                                                  c                          ⁢                                                      xe2x80x83                                                    ⁢                                                      (                            k                            )                                                                          ;                                                                                                            ρ                              vv                                                        ⁢                                                          xe2x80x83                                                        ⁢                                                          (                              k                              )                                                                                =                                                      δ                            ⁢                                                          xe2x80x83                                                        ⁢                                                          (                              k                              )                                                                                                                          ]                                                                      "RightBracketingBar"                            2                                                          (        3        )                                          xe2x80x83                ⁢                  =                                                                   c                ⁢                                  xe2x80x83                                ⁢                                  (                  k                  )                                                            arg                ⁢                                  xe2x80x83                                ⁢                min                                      ⁢                          xe2x80x83                        ⁢                                          ∑                                  n                  =                                      n0                    +                    L                                                                    n0                  +                  M                  -                  1                                            ⁢                              xe2x80x83                            ⁢                                                "LeftBracketingBar"                                                            r                      ⁢                                              xe2x80x83                                            ⁢                                              (                        n                        )                                                              -                                                                  ∑                                                  k                          =                          0                                                                          L                          -                          1                                                                    ⁢                                              xe2x80x83                                            ⁢                                              c                        ⁢                                                  xe2x80x83                                                ⁢                                                  (                          k                          )                                                ⁢                                                  xe2x80x83                                                ⁢                        s                        ⁢                                                  xe2x80x83                                                ⁢                                                  (                                                      n                            -                            k                                                    )                                                                                                      "RightBracketingBar"                                2                                                                        (        4        )            
where {circumflex over (r)}[n|nxe2x88x921;c(k);xcfx81vv(k)] is the one-step ahead prediction of r(n) given {r(k):k less than n}, {s(k):kxe2x89xa6n} and the channel coefficients c(k). It is further based on the assumption that the signal disturbance is white noise, in other words, that the auto-correlation of the disturbance xcfx81vv(k)=xcex4(k). When the noise v(n) is not white (i.e. xcfx81vv(k)xe2x89xa0xcex4(k)), the least-squares estimate defined in equation (4) is not expected to be the maximum likelihood (ML) estimate of c(k).
In a typical cellular system, the disturbance v(n) can be modeled as the sum of three signals passed through the analog receive filter p(t):
v(t)=[vco(t)+vadj(t)+vTH(t)]*p(t)xe2x80x83xe2x80x83(5)
v(n)=v(nxc3x97Tsymbol),xe2x80x83xe2x80x83(6)
where vco(t) is the analog co-channel interferer before the receive filter; vadj(t) is the analog adjacent channel interferer before the receive filter; vTH(t) is the thermal noise before the receive filter; and p(t) is the analog receive filter. Finally, v(n) is obtained by sampling v(t) every Tsymbol seconds.
Note that v(n) might become colored because vco(t) or vadj(t) can be colored. Moreover, v(n) might become colored because p(t) is not a Nyquist filter. In other words, the signal disturbance v(n) may become colored and the color of the disturbance may change from burst to burst of the communications signal. A colored signal disturbance may result in degraded performance because, as noted above, once the disturbance is colored, the ML estimate of the channel coefficients is typically not the least-squares estimate defined in equation (4).
According to embodiments of the present invention, methods, systems and receiver devices are provided which may provide improved receiver performance in obtaining estimates of the complex-valued baseband channel in the presence of colored baseband noise. The standard Least Squares (LS) channel estimation method may result in a suboptimal channel estimate when the baseband noise is colored as this method generally assumes that the noise is white. In some embodiments of the present invention, systems and methods are provided in which, over each synchronization signal period or other determinate information window, the channel coefficients and the color of the baseband noise are concurrently estimated. Thus, both the channel coefficients and the color of the noise are estimated rather than assuming white noise and providing channel coefficients that account for the color of the noise These estimates may be provided for each burst of a communication and may result in an improved channel estimate in the presence of colored noise. The baseband noise can become colored due to, for example, having a non-Nyquist receive filter, due to the presence of a colored co-channel interferer, or due to the presence of an adjacent channel interferer. The concurrent estimates of the color of the noise and channel coefficients may be provided iteratively or by selection of a best result among a plurality of candidate noise color assumptions in various embodiments.
In embodiments of the present invention, methods are provided for receiving a communication signal subject to colored noise over a communication channel. The communication signal including the colored noise is received at a receiver device. A channel estimate for the communication channel is determined based on the received signal, predetermined information associated with the received signal and an estimated color characteristic of the colored noise. A signal estimate for the received signal is generated using the determined channel estimate. The channel estimate may be determined using a generalized least squares algorithm. In alternative embodiments, the channel estimate may be determined by selecting a maximum likelihood one of a plurality of candidate channel estimates as the channel estimate, where each of the plurality of candidate channel estimates is based on one of a plurality of candidate noise color characteristic of the colored noise. The color characteristic of the colored noise may be an auto-correlation of the colored noise. The predetermined information may be a synchronization signal.
In other embodiments, a channel estimate is determined as follows. An initial channel estimate is generated based on an assumed auto-correlation, such as white noise, the received signal and the predetermined information. An updated auto-correlation is generated based on the initial channel estimate, the received signal and the predetermined information. An updated channel estimate is generated based on the updated auto-correlation, the received signal and the predetermined information. The initial channel estimates may be least squares channel estimates. The channel estimates are preferably channel coefficients. The generation of initial channel coefficients, an updated auto-correlation and updated channel coefficients is preferably repeated for a selected number of iterations. A predetermined number of iterations may be used or operations may repeat until a performance criteria is satisfied.
In other embodiments, the initial channel coefficients are generated using the equation:             c      ^        ⁢          xe2x80x83        ⁢          (      k      )        =                           c        ⁢                  xe2x80x83                ⁢                  (          k          )                            arg        ⁢                  xe2x80x83                ⁢        min              ⁢          xe2x80x83        ⁢                  ∑                  n          =                      n0            +            L                                    n0          +          M          -          1                    ⁢              xe2x80x83            ⁢                        "LeftBracketingBar"                                    r              ⁢                              xe2x80x83                            ⁢                              (                n                )                                      -                                          r                ^                            ⁡                              [                                                      n                    |                                          n                      -                      1                                                        ;                                      c                    ⁢                                          xe2x80x83                                        ⁢                                          (                      k                      )                                                        ;                                                                                    ρ                        vv                                            ⁢                                              xe2x80x83                                            ⁢                                              (                        k                        )                                                              =                                          δ                      ⁢                                              xe2x80x83                                            ⁢                                              (                        k                        )                                                                                            ]                                              "RightBracketingBar"                2            
where {circumflex over (r)}[n|nxe2x88x921;c(k);xcfx81vv(k)] is a one-step ahead prediction of r(n) given {r(k):k less than n}, {s(k):kxe2x89xa6n}, channel coefficients c(k) and the noise auto-correlation xcfx81vv(k)=xcex4(k). The updated auto-correlation may be generated using the equation:                     ρ        ^            vv        ⁢          xe2x80x83        ⁢          (      l      )        =            1              M        -        L              ⁢          xe2x80x83        ⁢                  ∑                  n          =                      n0            +            L                                    n0          +          M          -          1          -          l                    ⁢              xe2x80x83            ⁢                        (                                    r              ⁢                              xe2x80x83                            ⁢                              (                                  n                  +                  l                                )                                      -                                          ∑                                  k                  =                  0                                                  L                  -                  1                                            ⁢                              xe2x80x83                            ⁢                                                c                  ^                                ⁢                                  xe2x80x83                                ⁢                                  (                  k                  )                                ⁢                                  xe2x80x83                                ⁢                s                ⁢                                  xe2x80x83                                ⁢                                  (                                      n                    +                    l                    -                    k                                    )                                                              )                ⁢                  xe2x80x83                ⁢                              (                                          r                ⁢                                  xe2x80x83                                ⁢                                  (                  n                  )                                            -                                                ∑                                      k                    =                    0                                                        L                    -                    1                                                  ⁢                                  xe2x80x83                                ⁢                                                      c                    ^                                    ⁢                                      xe2x80x83                                    ⁢                                      (                    k                    )                                    ⁢                                      xe2x80x83                                    ⁢                  s                  ⁢                                      xe2x80x83                                    ⁢                                      (                                          n                      -                      k                                        )                                                                        )                    *                    
where {circumflex over (xcfx81)}vv(l) is an estimate of the l-the auto-correlation lag of the disturbance v(n), l is the auto-correlation lag, M is the number of known transmitted symbols, L is the length of the channel estimate (such as the number of channel coefficients), n0 is the index of the first known transmitted symbol, ĉ(k) is a previously obtained channel estimate, r(n) is the discrete-time received signal and s(n) are the known transmitted symbols. The updated channel coefficients may be generated as follows. A whitening filter for the colored noise may be formed based on the updated auto-correlation. The received signal and the predetermined information associated with the received signal may be filtered using the determined whitening filter and updated channel coefficients may be generated based on the filtered received signal, the filtered predetermined information associated with the received signal and the updated auto-correlation using the equation:             c      ^        ⁢          xe2x80x83        ⁢          (      k      )        =                           c        ⁢                  xe2x80x83                ⁢                  (          k          )                            arg        ⁢                  xe2x80x83                ⁢        min              ⁢          xe2x80x83        ⁢                  ∑                  n          =                      n0            +            L            +            q                                    n0          +          M          -          1                    ⁢              xe2x80x83            ⁢                        "LeftBracketingBar"                                                    r                xe2x80x2                            ⁢                              xe2x80x83                            ⁢                              (                n                )                                      -                                          ∑                                  k                  =                  0                                                  L                  -                  1                                            ⁢                              xe2x80x83                            ⁢                              c                ⁢                                  xe2x80x83                                ⁢                                  (                  k                  )                                ⁢                                  xe2x80x83                                ⁢                                  s                  xe2x80x2                                ⁢                                  xe2x80x83                                ⁢                                  (                                      n                    -                    k                                    )                                                              "RightBracketingBar"                2            
where rxe2x80x2(n) is r(n) filtered by the whitening filter, sxe2x80x2(nxe2x88x92k) is s(n) filtered by the whitening filter and delayed by k samples and q+1 is the length of the whitening filter. A finite impulse response whitening filter may be used.
In further embodiments, the communication signal comprises a plurality of bursts and wherein the predetermined information associated with the received signal is a synchronization signal included in each of the plurality of bursts. The channel estimate for the communication channel may be determined for each respective burst based on the synchronization signal included in the respective burst to provide a channel estimate associated with the respective burst. The signal estimate for the received signal may be generated for each respective burst using the channel estimate associated with the respective burst.
In other embodiments of the present invention, a plurality of candidate channel estimates, preferably channel coefficients, are generated. Each of the plurality of candidate channel estimates is based on one of a plurality of candidate auto-correlations. One of the plurality of candidate channel estimates is selected as the channel estimate. The plurality of sets of channel coefficients may be generated as follows. One of the plurality of candidate auto-correlations may be selected and a whitening filter may be determined based on the selected one of the plurality of auto-correlations. The received signal and the predetermined information associated with the received signal may be filtered using the determined whitening filter. One of the plurality of sets of channel coefficients may be generated based on the filtered received signal and the filtered predetermined information associated with the received signal. Operations may be repeated selecting, determining a whitening filter, filtering and generating one of the plurality of sets of channel coefficients for others of the plurality of candidate auto-correlations to provide the plurality of sets of channel coefficients.
In further embodiments of the present invention, each of the plurality of sets of channel coefficients {ĉi(k)}i=1N, where N is the number of candidate autocorrelations and i indicates the particular set of channel coefficients that is based on one of the plurality of candidate autocorrelations, may be generated using the equation:                               c          ^                i            ⁢              xe2x80x83            ⁢              (        k        )              =                                     c          ⁢                      xe2x80x83                    ⁢                      (            k            )                                    arg          ⁢                      xe2x80x83                    ⁢          min                    ⁢              xe2x80x83            ⁢                        ∑                      n            =                          n0              +              L              +                              q                i                                                          n0            +            M            -            1                          ⁢                  xe2x80x83                ⁢                              "LeftBracketingBar"                                                            r                  i                  xe2x80x2                                ⁢                                  xe2x80x83                                ⁢                                  (                  n                  )                                            -                                                ∑                                      k                    =                    0                                                        L                    -                    1                                                  ⁢                                  xe2x80x83                                ⁢                                  c                  ⁢                                      xe2x80x83                                    ⁢                                      (                    k                    )                                    ⁢                                      xe2x80x83                                    ⁢                                      s                    i                    xe2x80x2                                    ⁢                                      xe2x80x83                                    ⁢                                      (                                          n                      -                      k                                        )                                                                        "RightBracketingBar"                    2                      ,
where rixe2x80x2(n) is r(n) filtered by the whitening filter associated with the selected candidate autocorrelation, sixe2x80x2(nxe2x88x92k) is s(n) filtered by the whitening filter and delayed by k samples, and qi+1 is the length of the whitening filter. For each candidate channel estimate ĉi(k) obtained above, an associated squared-error may be computed according to the equation:       ϵ    i    =            ∑              n        =                  n0          +          L          +                      q            i                                      n0        +        M        -        1              ⁢          xe2x80x83        ⁢                            "LeftBracketingBar"                                                    r                i                xe2x80x2                            ⁢                              xe2x80x83                            ⁢                              (                n                )                                      -                                          ∑                                  k                  =                  0                                                  L                  -                  1                                            ⁢                              xe2x80x83                            ⁢                                                                    c                    ^                                    i                                ⁢                                  xe2x80x83                                ⁢                                  (                  k                  )                                ⁢                                  xe2x80x83                                ⁢                                  s                  i                  xe2x80x2                                ⁢                                  xe2x80x83                                ⁢                                  (                                      n                    -                    k                                    )                                                              "RightBracketingBar"                2            .      
The final channel estimate may be selected as the candidate channel estimate whose associated squared-error xcex5i is the smallest. In further embodiments, the whitening filters for each of the plurality of candidate auto-correlations may be generated in advance and stored and a respective one of the stored whitening filters may be selected as the whitening filter for each iteration of generating a candidate set of channel estimates such as channel coefficient sets.
In still further embodiments of the present invention, a receiver device is provided including a receiver that receives wireless communication signals, including a signal disturbance having an associated noise color, and downsamples the received signals to a symbol rate of the communication signals to provide received signal samples. The receiver device further includes an equalizer that generates symbol estimates from the received signal samples, the equalizer having associated channel coefficients, and a channel estimator that generates the channel coefficients based on the received wireless communication signals, predetermined information associated with the received wireless communication signals and the associated noise color of the signal disturbance.
The channel estimator may be further configured to iteratively estimate the channel coefficients and the associated noise color by setting at least one of the channel coefficients and the associated noise color to a value generated in a previous iteration and solving for the other of the channel coefficients and the associated noise color and using the other of the channel coefficients and the associated noise color as the value generated in a previous iteration in a subsequent iteration. In other embodiments, the receiver device further includes a memory configured to store a plurality of candidate auto-correlations and the channel estimator is further configured to generate channel coefficient sets based on each of the plurality of candidate auto-correlations and to select one of the generated channel coefficient sets as the channel coefficients.
As will further be appreciated by those of skill in the art, while described above primarily with reference to method aspects, the present invention may also be embodied as systems.